Báo cáo hóa học: "PERIODIC SOLUTIONS OF SECOND-ORDER NONAUTONOMOUS DYNAMICAL SYSTEMS" pptx

... θ||sinθ| (4−p)/p PERIODIC SOLUTIONS OF SECOND-ORDER LIÉNARD EQUATIONS WITH p-LAPLACIAN-LIKE OPERATORS YOUYU WANG AND WEIGAO GE Received 12 April 2005; Accepted 10 August 2005 The existence of periodic solutions for second-order ... existence of a unique nontrivial periodic solution to a class of equations of Li ´ enard’s type,JournalofDiff erential Equa- tions 46 (1982), no....

Ngày tải lên: 22/06/2014, 22:20

... case of uniqueness, the dissipative system (1.1) admits at least 6 Dissipative systems of the implied τ-periodic solution of (1.1) or a lower estimate of the number of τ-periodic solutions of (1.1), ... Proceedings of the National Academy of Sciences of the United States of America 53 (1965), 1262–1264. [23] N. Levinson, Transformation theory of non-linear differential...

Ngày tải lên: 22/06/2014, 22:20

... (y,ay−x). The simplicity of T gives no hint of the startling complexity shown by scatter plots of some of the solutions. See Figures 4.1–4.4,below. 2. Qualitative b ehavior of solutions Henceforth, ... establish the periodicity of all solutions to (1.1)seems novel, elegant, and of potentially wider applicability. Without this method, we could not prove that solutions o...

Ngày tải lên: 22/06/2014, 22:20

... existence of periodic solutions of discrete difference equations,Uzbekski ˘ ı Matematicheski ˘ ı Zhurnal (1995), no. 3, 88–90 (Russian). [10] Kh. Turaev, On the existence and uniqueness of periodic solutions ... research was supported by the Kamea Fund of the Israel Ministry of Science and Technology. References [1] S. S. Cheng and G. Zhang, Positive periodic solutions of a d...

Ngày tải lên: 22/06/2014, 22:20

... 0. (1.13) PERIODIC SOLUTIONS OF SECOND-ORDER NONAUTONOMOUS DYNAMICAL SYSTEMS MARTIN SCHECHTER Received 13 March 2006; Rev ised 10 May 2006; Accepted 15 May 2006 We study the existence of periodic solutions ... methods allow us to improve the previous results. 2. Proofs of the theorems We now give t h e proof of Theorem 1.1. Proof. Let X be the set of vector functions x(t)g...

Ngày tải lên: 22/06/2014, 22:20

... is just the repetition of the proof of Lemma 3.2, we omit the details of its proof. With the aid of above preparations, now we will give the proof of Theorem 1.2. Proof of Theorem 1.2 By(1.8), ... similar to the proof of Lemma 3.1, so we omit the details of its proof. Lemma 3.4 Under the conditions of Theorem 1.2, F (x) satisfies the PS condition. Proof From the proof of Le...

Ngày tải lên: 20/06/2014, 04:20

... 2011:58 http://www.advancesindifferenceequations.com/content/2011/1/58 Page 6 of 12 3 Canonical forms of self-adjoint second-order equations with polynomial coefficients Let us now determine the operators for which there is a basis of orthogonal eigenpoly- nomials ... include a proof for the readers’ convenience and because it is the main point in computation of norms of eigenfunc...

Ngày tải lên: 20/06/2014, 22:20

... follows from ( 1 ) which are appeared in the proof of Theorem 1.2. Then the proof of Theorem 1.3 is completed. □ Proof of Theorem 1.4. From the proof of Theorem 1.1, we know that  is coercive which ... completes the proof. □ 3 Proof of main results For the sake of convenience, we will denote various positive constants as C i , i =1,2, 3, Now, we are ready to proof our main resul...

Ngày tải lên: 21/06/2014, 00:20

... of first-order partial differential equations, including questions such as estimates of solutions of initial problems, estimates of domains of solutions, estimates of the difference between solutions ... Journal of Inequalities and Applications 2011, 2011:15 http://www.journalofinequalitiesandapplications.com/content/2011/1/15 Page 3 of 20 functions of one variable, whi...

Ngày tải lên: 21/06/2014, 02:20